Fire extinguishing systems of this kind have been known for quite a long time through prior use. They comprise a pressure vessel comprising a fire extinguishing medium such as for example N2, the fire extinguishing medium being stored in the pressure vessel under a pressure of up to several 100 bar. The pressure vessel is closed by a valve, to which a sensor line is connected for the automatic detection of a fire and for triggering an extinguishing process and to which an extinguishing line is connected for delivering the fire extinguishing medium during the extinguishing process. A pressure switch can be used to monitor the pressure in the fire extinguishing system and a signal generating system to be triggered as a function of the system pressure. The pressure switch can be connected directly to the valve.